The comparative energetics of the turtles and crocodiles

Abstract The Add‐my‐Pet collection of data on energetics and Dynamic Energy Budget parameters currently contains 92 species of turtles and 23 species of crocodiles. We discuss patterns of eco‐physiological traits of turtles and crocodiles, as functions of parameter values, and compare them with other taxa. Turtles and crocodiles accurately match the general rule that the life‐time cumulated neonate mass production equals ultimate weight. The weight at birth for reptiles scales with ultimate weight to the power 0.6. The scaling exponent is between that of amphibians and birds, while that for mammals is close to 1. We explain why this points to limitations imposed by embryonic respiration, the role of water stress and the accumulation of nitrogen waste during the embryo stage. Weight at puberty is proportional to ultimate weight, and is the largest for crocodiles, followed by that of turtles. These facts explain why the precociality coefficient, sHbp—approximated by the ratio of weight at birth and weight at puberty at abundant food—decreases with ultimate weight. It is the smallest for crocodiles because of their large size and is smaller for turtles than for lizards and snakes. The sea turtles have a smaller sHbp than the rest of the turtles, linked to their large size and small offspring size. We link their small weight and age at birth to reducing risks on the beach. The maximum reserve capacity in both turtles and crocodiles clearly decreases with the precociality coefficient. This relationship has not been found that clearly in other taxa, not even in other reptiles, with the exception of the chondrichthyans. Among reptiles, crocodiles and sea turtles have a relatively large assimilation rate and a large reserve capacity.


| INTRODUC TI ON
is an open access online collection of referenced data on animal energetics and Dynamic Energy Budget (DEB) parameters (AmP, 2021; Marques et al., 2018). The collection is run as a journal, meaning that everyone can contribute, and submissions are reviewed prior to acceptance. This study is part of a series of case studies on selected taxa from AmP whereby DEB parameters and associated traits are presented in eco-evolutionary context. It focusses on traits of turtles (Testudines) and crocodiles (Crocodilia), using other reptiles as a reference; previous studies were on fish Lika et al., 2022), petrels and penguins (Kooijman, 2020), carnivores and pangolins (Kooijman & Augustine, 2022a), cephalopods (Kooijman & Augustine, 2022b).
Eco-physiological traits are gaining more focus, as conservation physiology (sensu Cooke et al., 2013) is emerging as an 'increasingly integrated and essential science' (Cooke et al., 2013). Traits that are based on mechanistic models linking individuals to their environments can be used to predict how species respond to environmental change , but also to study evolutionary drivers (Beekman et al., 2019;Jusup et al., 2017). Add-my-Pet (AmP) collection presents an array of such traits, and is therefore a most valuable resource. Table 1 gives the number of reptile species currently included in the AmP collection, compared with the number of existing species. In our analysis and discussion, we use the Lepidosauria (= Rhynchocephalia + Squamata) and a dozen extinct reptile species ("dinosaurs") as reference. Analysis is focused on turtles and crocodiles because we consider them `complete' in the collection, that is, that it will be hard to find data on more species in open literature. The list of turtle and crocodile AmP species, the data types for each species and selected references can be found in the Appendix (Table A1 and Table A2).
This paper first introduces turtles and crocodiles, briefly presents the Dynamic Energy Budget (DEB) framework used to formalize the traits, then discusses aspects of energetics and life history, and finalizes with a Discussion and conclusion section.

| REP TILE S , TURTLE S AND CRO COD ILE S
The extant "reptiles" are a polyphyletic group, with the 4 main lineages usually described as crocodilians, turtles, squamates (snakes and lizards), and tuatara. The name Reptilia is nowadays less frequently used, because it is not a clade (Shine, 2013). It should include birds, which, together with the crocodiles, form the clade Archosauria.
Turtles and crocodiles are placed in the clade Archelosauria, while the "true" reptiles are a sister clade: the Lepidosauria (tuatara, lizards and snakes). Despite the exact grouping being still open to debate (Hedges & Poling, 1999), it is evident that reptiles have been independently evolving into very different animals since the Triassic (Hedges & Poling, 1999). We here focus on turtles (Testudines) and crocodiles (Crocodilia), but compare them with tuatara, squamates (Lepidosauria), and extinct reptiles present in the AmP collection (Pterosauria, Saurischia, Ornithischia, and Tyrannosauridae).
All turtles and crocodiles lay eggs, which, unlike many squamates which made the transition to ovovivipary, prevents them from living in cooler climates. Like most reptiles, they are ectothermic and master the art of regulating their body through behavior excellently. Interestingly, evidence exists for endothermy in the ancestors of the crocodiles, which converted back to ectothermy when adopting an aquatic life style (Seymour et al., 2004), and sea turtles are partially (Mrosovsky, 1980;Standora, 1982). Most turtles and all crocodiles have temperature dependant sex determination (Lee et al., 2019;Valenzuela & Adams, 2011), even though some turtles reverted to gene sex determination. The latter enables living in colder conditions, and is present also in all snakes. By contrast, the temperature-dependant sex determination can also be found in some lizards, but not in habitats with extreme temperature fluctuations (Pen et al., 2010).
Some 60% of the turtle species are presently considered to be threatened (Rhodin et al., 2018), while of the 24 crocodile species, the IUCN crocodile specialist group lists 7 species as critically endangered and 12 species as vulnerable (IUCN-Crocodile-Specialist-Group, 2021). The main threats, for turtles and crocodiles alike, are global climate change, habitat destruction, and illegal hunting, with (plastic) pollution as an emerging pressure for all wildlife, especially marine species such as sea turtles (Gall & Thompson, 2015;Marn et al., 2020;Nelms et al., 2016;Schuyler et al., 2014). Conservation in a changing world needs predictive mechanistic models (Wood et al., 2018), and functional traits derived from mechanistic models are invaluable in determining a species niche (Kearney & Porter, 2009). DEB theory has already been used to evaluate effects of climate change and plastic ingestion on sea turtles Stubbs et al., 2017) and to optimize site selection for the western swamp turtle re-introduction programs (Arnall et al., 2014(Arnall et al., , 2019, and to explain geographic shifts in reproductive patterns of a viviparous lizard (Schwarzkopf et al., 2016).
We hope that this paper contributes to a better understanding of the eco-physiology of turtles and crocodiles, and, in a much broader context, brings us closer to tackling major questions in ecology and evolutionary biology (Kearney et al., 2010).

| DEB MODEL S AND TR AITS
Dynamic Energy Budget models aim to quantify the various aspects of energy and mass budgets in dynamic environments in terms of TA B L E 1 The number of reptile species in the AmP collection at time of the analysis (2022/04/04), the number of extant species (estimates from Wikipedia) and the coverage for reptile classes. Rhynchocephalia and Squamata form the class Lepidosauria, and are for simplicity presented as such in subsequent analysis In the context of DEB theory, we define a trait as "a parameter or a function of parameters, which quantifies some eco-physiological property of a species" . We followed the workflow that (measured) data from literature was used to estimate parameters, and these parameters are used to quantify the traits.

| Multidimensional scaling
Supplementary to analyzing distribution of traits and patterns in the co-variation of parameter values, we have applied multidimensional scaling (MDS) on trait-based distances between species . We chose 12 traits from those analyzed in this study (see

| ENERG E TI C S AND LIFE HIS TORY
We first present the distribution of selected eco-physiological traits for the turtles, crocodiles and Lepidosauria (squamates and tuatara), and then discuss some features in more detail. All temperature dependent traits are presented at a common reference temperature of 20°C. Figure 1 shows survivor curves for selected traits, that is, for each trait the fraction of species for which the trait value exceeds the value on the abscissa. This is a very simple representation but can already point to general patterns and main differences or similarities between the groups. We here discuss the coherence.

| Distributions of traits
The specific assimilation rate ṗ Am of crocodiles is much larger than that of turtles and squamates ( Figure 1a). This, combined with a smaller specific maintenance ṗ M (Figure 1d), explains in part why their ultimate weight is much larger (Figure 1i). See also Figure 4.
The energy conductance of turtles and crocodiles is quite a bit larger than that of squamates ( Figure 1b). The effect of a large specific assimilation dominates that of a relatively large energy conductance in the maximum reserve capacity (Figure 1f), which equals the ratio of the two, and is the largest for crocodiles, implying they can sustain well the periods of starvation. An increase in energy conductance and in somatic maintenance both enhance growth. This is because the energy conductance determines the mobilization flux of reserve and the von Bertalanffy growth rate works out to be proportional to the specific somatic maintenance rate in the DEB F I G U R E 1 Survivor curves for selected DEB parameters and other traits for reptile taxa in the AmP collection: Testudines (blue), Crocodilia (red), Lepidosauria (black); for number of species see Table 1. Ages at birth, puberty and death are presented on the same plot; same for weights. All traits are presented for a body temperature of 20°C context. (The specific growth rate at maximum growth turns out to equal 1.5 times the von Bertalanffy growth rate, see Kooijman et al., 2020.) Therefore, a large energy conductance combined with a small specific somatic maintenance can result in the same von Bertalanffy growth rate as vice versa. The effect of the energy conductance on growth is, however, more restricted, which explains why maximum specific growth is small in turtles and crocodiles (Figure 1j), despite their large energy conductance.
The allocation fraction to soma is similar in the three taxa, with the crocodiles having a slightly higher median value than the other two taxa (Figure 1c). This is in accordance with the highest ultimate weight of this class, as the ultimate size is proportional to .
A large energy conductance (Figure 1b) leads to a short incubation time, that is, smaller age at birth, but this is not what we observe ( Figure 1e) because absolute egg size matters as well. Egg size is the largest for crocodiles, followed by that of turtles ( Figure 1i).
The eggs and hatchlings of the crocodiles may be the largest among reptiles; however, they are relatively the smallest when the size of the parent is taken into account. This information is expressed as the precociality coefficient, which for crocodiles is lower than for turtles and much lower than for squamata ( Figure 1g). The precociality coefficient, s bp H , is a ratio of maturities at birth and puberty, but it roughly equals the ratio of the weights at birth and puberty at abundant food . We will see that the weight at puberty is approximately proportional to ultimate weight, but that at birth scales with ultimate weight to the power 0.6. This implies that the differences in the precociality coefficient is mainly due to differences in adult weight.
The supply stress, s s , is defined as maturity maintenance times squared somatic maintenance, divided by cubed assimilation and can take values between 0 and 4/27. It is similarly low for the three taxa (Figure 1h), meaning that they can rather easily deal with low food conditions and respond with low growth and reproduction . Birds and mammals have the highest supply stress, insects the lowest. Among reptiles, the median value is highest for turtles (0.0321), followed by that for crocodiles (0.0275), and then lepidosauria (0.0168). Sea turtles, perhaps due to their partial

| Respiration, life span, and reproduction
Respiration, life span, and reproduction are intimately connected for turtles and crocodiles (and other reptiles) (Figures 2 and 3), as found for chondrichthyans  and for actinopterigyans (Lika et al., 2022). The relationships apply, with much more scatter, to all 3000 animal species in the AmP collection that covers all larger phyla . The life span is inverse to the specific respiration ( Figure 2a) and the life-time cumulated neonate mass production equals the ultimate weight (Figure 3a). Long life, implying a long period of reproduction, offsets the relatively small egg size and offspring size of turtles and crocodiles (Figure 3b). We come back to the small egg size of turtles and crocodiles in the discussion. The lines shown in the figures have not been fitted to the data; no parameters involved. Figure 2b shows that Kleiber's law also applies to reptiles, as explained by the physical co-variation rules of DEB theory (Kooijman, 1986a(Kooijman, , 2010. DEB theory does not work with allometric relationships. Specific respiration at abundant food works out as a cubic polynomial in ultimate length (Kooijman, 2010), but when curvature is ignored in a log-log plot, the slope is close to −1/4, which is what we plotted in the plot (Figure 2b). The respiration of crocodiles, and the rather low one for turtles, fits the relationship well, meaning that their low respiration is mostly due to their large size. Body size is, in the context of DEB theory, an emergent property of metabolism, not an independent variable . So the figure shows how one function of DEB parameters relates to another function of these parameters.

| Precociality coefficient and size at birth and puberty
Size is, in large part, a result of the ratio between how much energy is assimilated and how much energy is left after maintenance needs have been met; turtles and crocodiles have relatively small maintenance costs relative to assimilation capacity, compared with other reptiles ( Figure A2a in the Appendix). While some squamata are tiny, there are no very small turtles or crocodiles; the smallest living turtle is Chersobius signatus of 172 g; this is visible also in weight distribution Figure 1i. Figure 4a shows that weight at puberty is directly proportional to ultimate weight (as expected by the physical co-variation rules of DEB theory), with a fixed fraction 0.4. However, weight at birth scales to ultimate weight to the power 0.6, not only for turtles and crocodiles, but for all reptiles. Ratio of weight at birth and weight at puberty approximates to the precociality coefficient.
The physical co-variation rules predict that the precociality coefficient roughly equals the weight at birth over that at puberty at abundant food, while the latter is more or less proportional to ultimate weight. We expect the precociality coefficient to scale with ultimate weight to the power −0.6, because birth weight was found to be proportional to ultimate weight to the power 0.6. This approximates what we did find (Figure 4b). The precociality coefficient is the smallest for crocodiles when classes are compared (Figure 1g), however, that of sea turtles is even smaller (see e.g., Figure 5d, and Figure A3 in the Appendix). The precociality coefficient quantifies how 'immature' an offspring is born, and is calculated as a ratio of maturity at birth and puberty. For reptiles, we can draw direct links to the egg size relative to adult size. We come back to this in the discussion.
F I G U R E 4 Panel (a): Weight at birth and at puberty as functions of ultimate weight. Panel (b): Precociality coefficient, s bp H , as function of ultimate weight. Weight at puberty scales proportionally with ultimate weight (slope of 1), whereas weight at birth scales with a slope of 0.5818. The decrease of the precociality coefficient with ultimate weight follows from the previous scaling, since s bp H can be approximated by the ratio of weight at birth and weight at puberty. Markers as in Figure 2: turtles -blue circles; crocodiles -red triangles; other reptiles -black dots 4.4 | Reserve capacity Figure 5 shows (in sub-figure a) that the maximum reserve capacity E m is proportional to the surface area-specific assimilation rate ṗ Am ; this is easy to understand since E m = ṗ Am ∕v. The physical co-variation rules imply that E m is also proportional to maximum structural length, that is, to ultimate weight after some contribution of reserve is taken into account. This link, however, is not clearly visible for reptiles (Figure 5b). Maximum reserve capacity was found to increase with ultimate weight in chondrichthyans , but not in actinopterigyans (Lika et al., 2022), which was explained by interference with the waste-to-hurry pattern (Kooijman, 2013). We do not think, however, that this pattern explains the lack of co-variation between maximum reserve capacity and maximum weight here, since specific somatic maintenance ṗ M is too small to drive specific assimilation up, and the range for ṗ M is rather small for turtles and crocodiles. Energy conductance, vwhich is also affected in species with the waste-to-hurry pattern (Kooijman, 2013), and is the other parameter defining the E m -has some scatter, but does not have a clear link to maximum weight ( Figure A2b in the Appendix).
Maximum reserve capacity increases with specific somatic maintenance ṗ M , Figure 5c, which is also part of the reason why the relationship between E m and ultimate weight is less clear: ṗ M reduces maximum structural length, so maximum weight. The ecological functionality of the co-variation of maximum reserve capacity with specific somatic maintenance obviously helps to cope with temporary dips in food availability, although many turtle and crocodile species can enter torpor states.
Maximum reserve capacity tends to decrease with the precociality coefficient, s bp H , although with considerable scatter (Figure 5d), which seems to be unique for turtles and crocodiles; we did not see this pattern before that clearly. The reason is probably that the scatter in the relative weights at birth and puberty is small (Figure 4a), so the signal is clear. We think that the existence of this pattern ( Figure 5d) implies that E m in fact does increase with ultimate weight also for reptiles, but that the latter relationship comes out less clearly because more parameters contribute to ultimate weight, leading to a large scatter which obscures the signal.

| Multidimensional scaling
We present results of multidimensional scaling (MDS) applied to reptiles for the following 12 eco-physiological traits, most of them analyzed also in the previous sections: age at birth and puberty (a b , a p ), life span (a m ), ultimate wet weight (W ∞ w ), reproduction rate at ultimate size (R i ), egg size (E 0 ), maximum reserve capacity ( E m ), energy conductance (v), volume-specific maintenance rate ( ṗ M ), area-specific maximum assimilation rate ( ṗ Am ), supply stress (s s ), and precociality coefficient (s bp H ). Multidimensional scaling clusters species in multidimensional space. We present here "only" a two-dimensional plot (Figure 6), but the eigenvalues in the bottom right corner of the figure indicate that the first two dimensions are the most relevant ones (third eigenvalue is already much smaller than the first and the second one; (squamates + tuatara) on the left, then Testudinidae (tortoises) and crodociles (Crocodilia) in the middle, and then remaining turtles (Testudines), with sea turtles (Chelonioidea) close to the far right ( Figure 6).
When correlating the traits with the first and second eigenvector, we see that the life span and age at puberty have the highest (−ve) correlation with the first eigenvector, followed by the (+ve) precociality coefficient (correlation coefficients larger than 0.7, 0.6, and 0.5, respectively). Maximum reserve capacity, somatic maintenance, and maximum assimilation have the highest (+ve) correlation with the second eigenvector (correlation coefficients larger than 0.5). This points to the main traits characterizing the analyzed groups, as we discuss in the following section.

| D ISCUSS I ON AND CON CLUS I ON S
Reptiles are a diverse polyphyletic group, but, as we have just shown, their eco-physiological traits also point to similarities in trait patterns, and coherence within and between groups.
Multidimensional scaling (MDS) on trait-based distances between species supplements our efforts to find patterns in the covariation of parameter values. We used most of the traits analyzed in this study (see Section 4.5 for a list of traits) to expand on the turtle-focused MDS presented in Kooijman et al. (2021). Results of the MDS analysis corroborate the grouping evident already in the simple co-variation analysis: in the multidimensional space crocodiles again cluster together, as do the turtles, both of them separate from the rest of the reptiles. Within turtles, sea turtles and tortoises form separate clusters ( Figure 6).
When using this specific selection of traits and correlating them to the first two eigenvectors, we can identify main characteristics (i.e., eco-physiological traits) which place species at either of the two extremes: at one of the extremes we have slow-maturing, long-living, relatively large individuals with relatively small offspring (i.e., a small precociality coefficient) and relatively high metabolism, but also good ability to withstand food shortages (high reserve capacity)such as sea turtles. At the other extreme, we have individuals with a relatively fast life cycle, and with offspring size more similar to parent size (i.e., a higher precociality coefficient), which are less tolerant to periods of starvation (i.e., they have a lower maximum reserve capacity)-such as lizards and snakes. This points to quite specific environmental pressures, and is therefore encouraging that related species experiencing similar environments cluster together.
Even though (ultimate) weight is not one of the traits with a strong correlation to one of the two axes in the MDS plot, the results section shows that it does have a strong relationship to many ecophysiological traits. Coupling of many eco-physiological traits to size (Calder, 1984;Peters, 1983) has well understood reasons (Kooijman, 2010); the fact that large weight allows for long starvation intervals and dives (for aquatic species) is very relevant in this context. Moreover, both turtles and crocodiles-frequently among the largest reptiles-easily switch to a estivation/torpor/hibernation state where they further reduce their maintenance costs (Hochscheid et al., 2007;Nussear et al., 2007;Staples, 2016).
Generally, crocodiles as a group have the slowest metabolism among reptiles (Figures 1 and 2), but their low respiration is matched-or even exceeded-by low respiration of large and long lived tortoises and sea turtles (Figure 2). Maximum specific growth rates of turtles are larger than that of crocodiles and smaller than that of other reptiles (Figure 1j), but there is much variation within the group (not shown): sea turtles (Chelonioidea) have a relatively large maximum specific growth rate, but their close relatives, the mud and musk turtles (Kinosternidae) have a relatively small maximum specific growth rate, a small ultimate weight and typical relative weight at birth. This seems to reflect opposing selection pressures within the Chelydroidea (Chelonioidea + Kinosternidae).
Specific respiration of turtles and crocodiles (as well as other reptiles) is inverse to their life span (Figure 2a), and life-time cumulative neonate mass production equals ultimate weight ( Figure 3b); a pattern also observed in fish Lika et al., 2022). In some reptile groups-such as sea turtles, and larger crocodiles and tortoises-the eggs and offspring are small relative to ultimate weight (Figure 3a). The fact that the equality between life-time cumulative neonate mass and ultimate weight holds also for these groups, suggests that the small offspring size is offset by a large number of offspring throughout the reproductive period. We discuss later the possible explanation for having such small offspring.
For both turtles and crocodiles (and reptiles in general), weight at puberty is directly proportional to ultimate weight, but the weight at birth as a fraction of ultimate weight decreases with ultimate weight substantially (Figure 4a). This calls for an explanation, and we do it in the context of other vertebrates: amphibia, birds, and mammals, but also fish. Figure 7 presents the behavior of the scaling exponent for weight at birth as a function of ultimate weight, for vertebrates that live on land. We focus on this scaling exponent because constraints of the type that we will consider become more apparent for increasing size. Birds have a scaling exponent of 0.8 , while their eggs-directly proportional to size at birth-are relatively larger than that of reptiles. Although the body size-range for birds is smaller than that of reptiles, the smaller scaling exponent for reptiles is probably not due to mechanical constraints of producing large eggs; the 3.9 kg kiwi has an egg size of even 20% of its body weight, implying that larger birds could lay larger eggs too. This view is confirmed by the exponent of placentalia of 0.946 , which produce neonates of similar relative size compared to birds, so larger than that of reptiles, while their range of body sizes exceeds that of reptiles. This points to explanations other than mechanical constraints: (i) limitation of respiration during the embryo stage, (ii) the accumulation of nitrogen waste in the egg, and (iii) water loss from the egg.
The placentalia escaped these problems by placental vivivary.
Dioxygen limitation was already suggested for amphibia, which produce aquatic eggs with jelly envelopes that might reduce transport of O 2 (Seymour & Bradford, 1995); they have a scaling exponent of 0.5 , so somewhat smaller than the reptiles. The biggest amphibians, i.e. the giant salamanders Andrias with the largest eggs, live in cold water, where respiration limitation is weaker due to low metabolic needs and high solubility of O 2 in cold water, and the produced nitrogen waste can easily dissipate. The nitrogen waste of amphibians is mainly ammonia in tadpoles, which is toxic, but they hardly suffer from this in an aquatic environment where ammonia can easily dissipate. Many chondrichthyans sport vivipary and their metabolic rate is less then that of birds, have relatively large neonates and a scaling exponent of 0.88 , between that of birds and placentalia. This suggests that they too escaped the selection pressure from oxygen limitation.
Terrestrial environments exert a strong selective pressure on water loss and nitrogen waste accumulation in eggs. Birds and reptiles are uricoletic (Withers, 1992), so they solved the nitrogen waste problem by making use of non-solvable (so non-toxic), but energetically expensive types of nitrogen waste. Birds have much higher metabolic rates than reptiles and use lipids as energy source, which give much more water than proteins when oxidized during metabolism. This allowed birds to insert larger pores in their egg shells, compared to reptiles, increasing the O 2 availability without loosing too much water. By contrast, reptiles primarily use proteins as energy source. They, therefore, need to preserve water in eggs better than birds, which they do by having smaller pores in egg shells, limiting O 2 availability and thus maximum egg size. Altricial birds that nest in trees show that water loss is an important issue; they hatch with extra water content in their tissues which reduces till fledging Konarzewski, 1988). This illustrates the conflicting needs of water and dioxygen transport for terrestrial eggs, and points to the conclusion that birds managed to escape these problems almost completely, in view of their scaling exponent being close the one, like was found for weights at puberty for all vertebrate taxa.
Relatively small eggs (and offspring) of some turtles and crocodiles ( Figure 3a) could be linked to specific ecological pressures.
Turtles and crocodiles make nests and bury their eggs in sand, where temperature depends on sunshine, or in a heap of dead leaves, where temperature depends on fungal activity. Incubation is timed when environmental conditions are favorable, and so the longer the incubation lasts-incubation duration increasing with egg size-the more difficult it becomes to select the proper time window, and the higher the risk of nest destruction. Shorter incubation times are also incentivized by the fact that nests are extremely vulnerable to predation, sea turtles being the prime example (Bolten et al., 2011;Whiting & Whiting, 2011). Although sea F I G U R E 6 Multidimensional scaling applied to all 243 reptiles in the collection, using 12 arbitrarily chosen eco-physiological traits (see text for list of traits). The bottom right figure presents all eigenvalues. The first 12 eigenvalues are presented in blue. Markers: Blue dots represent turtles (Testudines), with grey blue dots marking sea turtles (Chelonioidea) and empty blue dots tortoises (Testudinidae). Red triangles mark living crocodiles (Crocodilia), and the extinct Deinosuchus is marked with a red dot. Black dots represent squamates and tuatara (Lepidosauria), and grey dots a dozen extinct reptiles belonging to Pterosauria, Saurischia, Ornithischia, and Tyrannosauridae F I G U R E 7 Scaling exponent for weight at birth as a function of ultimate weight for amphibia, reptiles, birds, and mammals (Modified from Augustine et al., 2021). Size at birth (and therefore egg size) increases with ultimate weight, but less so for reptiles than for birds and mammals. We discuss this in the text turtles have parameters in the range of other turtles, within this range they have one of the smallest relative weight and age at birth, typical weight at puberty, and their ultimate weight is at upper end of the turtle range ( Figure 4). Large adult size corresponds to a large reproductive output. As a consequence of eggs being small, the number of eggs is relatively large (Figure 3); see also Beekman et al. (2019). We suggest that their small eggs and short incubation times are adaptations to minimize their stay on land to reduce the risks of flooding (Ewert, 1979), and predation. The latter interpretation is further supported by synchronized hatching, not only within a nest, but also between nests on the same beach. Details of beach conditions seem very important to the turtles, since the selection of nesting sites has a strong historic component which explains most of their long-distance migration behavior. Crocodiles have the same problem of very vulnerable early life stages, but solved it in a different way: by guarding their nest with a respectable set of teeth and substantial body mass. Their relative weights at birth and puberty are typical, but their ultimate mass is at the upper end of the range for the Archelosauria. For comparison, the exponent for oviparous and viviparous chondrichthyans is the same, which suggests that reduction of predatory risks by reducing eggs size, thus shortening incubation time, might be less important for chondrichthyans .
The comparison of life history traits between taxa is not without problems; it matters a lot how we compare exactly and what is taken as reference. For instance, when we suggest that dioxygen availability or toxicity of accumulated nitrogen waste limit embryo size, we do not imply that the embryo actually experiences such limitation or toxic effects, only that egg size is such that these problems are avoided.
The large literature on bird egg development stresses the role of O 2 limitation (Hoyt & Rahn, 1980;Tazawa et al., 1983;Visschedijk, 1968;Visschedijk & Rahn, 1983). The authors point that the maximum flux through the pores is egg-size independent, from hummingbird to ostrich, and point to the levelling of dioxygen consumption prior to pipping. This implies that O 2 is actually limited. If true, we disagree with this view. The constancy of maximum dioxygen flux through the pores is taken as a consequence of the need to minimize water loss: pores should not be larger than strictly necessary. The levelling of dioxygen consumption prior to hatching also occurs in very different species that do not have an egg shell (Kooijman, 1986b), and therefore cannot be caused by the limiting O 2 flux. DEB theory takes this as a result of depleting reserve, which not only causes a levelling of, but even a decline of dioxygen use prior to hatching, as is really clear in eggs of the pig-nosed turtle, Carettochelys insculpta, and the Australian freshwater crocodile, Crocodylus johnsoni (Zonneveld & Kooijman, 1993), where embryos delay hatching by waiting for their nest mates to be ready for synchronous hatching.
Coherence and consistency are crucial conditions for comparing eco-physiological traits within and between taxa, and we believe that using DEB model-derived traits greatly adds to both of these prerequisites . Furthermore, it bypasses the data limitations which are often imposed when a broader (or more in-depth) analysis is required (Wood et al., 2018), because (i) DEB models need relatively few data to parameterize (Marques et al., 2018), and (ii) all traits can be computed for all species for which DEB parameters have been estimated, which is currently over 3000 animal species (AmP, 2021). Analyzing trait patterns then further improves the process of parameter estimation for a species of interest, resulting in a better predictions and more in-depth knowledge about the species. Knowledge about metabolic performance under various external and internal pressures is key to conservation biology, sustainable management and environmental risk assessment, which are seen as interlinked fields with much to gain from coherent and applicable predictive models (Wood et al., 2018).

ACK N OWLED G EM ENTS
We like to thank all who contributed to the Add-my-Pet collection.

CO N FLI C T O F I NTE R E S T
The authors declare no conflict of interest.

DATA AVA I L A B I L I T Y S TAT E M E N T
The underlying data come from published literature. The data and the references to where it comes from can be found on the Addmy-Pet website https://www.bio.vu.nl/thb/deb/debla b/add_my_pet as well as on its mirror at https://debth eory.fr/add_my_pet/. There you can also find the code that has been used to estimate parameter values for each species. This code uses the software packages AmPtool AmP, 2021 and DEBtool DEBtool, 2021, which are freely available via Github: https://github.com/orgs/add-my-pet/repos itories. A selection of references to data for each species is also given in the Appendix.